Horses will never be able to see the world the way we do. The structure and position of their eyes is different than ours, which leads to differences in the distance, color, vividness and visual field that horses experience.
Horses do have the ability to see color, although not as vividly as we do. They are somewhat similar to colorblind people. However, their visual field is greater than ours: a horse's field of vision is nearly 360 degrees with only a small blind spot directly behind them.
People that have horses should learn more about the way they see; this will help them to safely handle their horses and work around them, as well as help to understand why horses’ behavior can changes in certain situations.